Skip to contents

Raw score to measure conversion table

Source: R/person.R
score_table.Rd

The score-to-logit conversion for complete responders: every possible raw score with its location, standard error, and the frequency and cumulative percentage of complete responders at that score (the complete-data estimates table of Andrich and Marais 2019, ch. 10).

Usage

score_table(
  fit,
  method = c("wle", "mle"),
  extremes = c("model", "extrapolated")
)

Arguments

fit

A fitted object from rasch.

method

"wle" (Warm, default) or "mle".

extremes

"model" keeps the estimator's own extreme-score values (NA for MLE); "extrapolated" applies the geometric extrapolation.

Value

A data frame with score, theta, se, freq, cum_pct (omitted when no complete responders exist), and extrapolated; NULL for fits without a common raw-score metric (EFRM).

Details

Two estimators are available. "wle" (the default) is Warm's weighted likelihood estimate, finite at the extreme scores. "mle" is the plain maximum likelihood estimate, infinite at the extremes. extremes = "extrapolated" replaces the extreme-score entries by the geometric extrapolation described in Andrich and Marais (2019, ch. 10): successive score-to-score differences grow towards the extremes, so the last difference is continued geometrically – the extrapolated top difference \(d\) solves \(b = \sqrt{a d}\) where \(a, b\) are the two preceding differences (equivalently \(d = b^2/a\)), and symmetrically at zero. The standard error at an extrapolated location is \(1/\sqrt{I(\theta)}\) evaluated there. With method = "wle" the extrapolation replaces the finite Warm estimates at the extremes, giving the extrapolated form of the conversion table from a WLE analysis.

Examples

set.seed(1)
d <- seq(-1.5, 1.5, length.out = 6)
X <- matrix(rbinom(300 * 6, 1, plogis(outer(rnorm(300), d, "-"))), 300, 6)
colnames(X) <- paste0("I", 1:6)
score_table(rasch(X), method = "mle", extremes = "extrapolated")
#>   score       theta        se extrapolated freq    cum_pct
#> 1     0 -3.27788845 1.8246799         TRUE   13   4.333333
#> 2     1 -1.95393671 1.1597821        FALSE   35  16.000000
#> 3     2 -0.88068333 0.9582186        FALSE   63  37.000000
#> 4     3 -0.01065703 0.9221359        FALSE   73  61.333333
#> 5     4  0.86803622 0.9667528        FALSE   66  83.333333
#> 6     5  1.96255223 1.1702696        FALSE   41  97.000000
#> 7     6  3.32590095 1.8484082         TRUE    9 100.000000